Recursive List Decoding for Reed-Muller Codes

TL;DR

This paper introduces two novel recursive decoding algorithms for Reed-Muller codes, demonstrating significant performance improvements and near-optimal decoding at moderate code lengths with feasible complexity.

Contribution

The paper presents new recursive decoding techniques for Reed-Muller codes and their subcodes, with asymptotic analysis and practical enhancements for improved performance.

Findings

Algorithms outperform existing nonexponential complexity decoders

Near-optimal decoding achieved for code lengths up to 512

Performance improved with intermediate code lists and permutation procedures

Abstract

We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding algorithms with nonexponential complexity known for RM codes. Decoding performance is further enhanced by using intermediate code lists and permutation procedures. For moderate lengths up to 512, near-optimum decoding with feasible complexity is obtained.